Block #437,173

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/10/2014, 3:02:44 AM · Difficulty 10.3577 · 6,361,849 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

96e7529a1dcb0fe5adaf49cb74fafdc049b6403d3063fe20e018577946d9238b

View on Chainz ↗

Height

#437,173

Difficulty

10.357706

Transactions

Size

1.01 KB

Version

Bits

0a5b929a

Nonce

69,787

Timestamp

3/10/2014, 3:02:44 AM

Confirmations

6,361,849

Mined by

⛏️ aS+JAGD4yZQwygGFSCiBcSnuDhf75LhGzM2XAx

Merkle Root

e327889609ad4002a58b4bef6e95ac9a3d69f862269c318c900014cb489e4313

Transactions (1)

Coinbasee327889609ad40…0014cb489e4313

1 in → 26 out9.3100 XPM947 B

AGD4yZQw…hGzM2XAx Aac9Hjdg…P4ktypc3 AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

8.319 × 10⁹⁴(95-digit number)

83195368984371845565…82510525200102566399

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

8.319 × 10⁹⁴(95-digit number)

83195368984371845565…82510525200102566399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.319 × 10⁹⁴(95-digit number)

83195368984371845565…82510525200102566401

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

1.663 × 10⁹⁵(96-digit number)

16639073796874369113…65021050400205132799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.663 × 10⁹⁵(96-digit number)

16639073796874369113…65021050400205132801

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

3.327 × 10⁹⁵(96-digit number)

33278147593748738226…30042100800410265599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.327 × 10⁹⁵(96-digit number)

33278147593748738226…30042100800410265601

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

6.655 × 10⁹⁵(96-digit number)

66556295187497476452…60084201600820531199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.655 × 10⁹⁵(96-digit number)

66556295187497476452…60084201600820531201

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

1.331 × 10⁹⁶(97-digit number)

13311259037499495290…20168403201641062399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.331 × 10⁹⁶(97-digit number)

13311259037499495290…20168403201641062401

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆

Rarity

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer